Turkish Journal of Mathematics
Abstract
We establish necessary and sufficient conditions on a weight v governing the trace inequality \hat{K}f _{L^q_v(\hat{E})} \leq C f _{L^p(E)}, where E is a cone on a homogeneous group, \hat{E}: = E \times R_+ and \hat{K} is a positive kernel operator defined on \hat{E}. Compactness criteria for this operator are also established.
DOI
10.3906/mat-1209-21
Keywords
Operators with positive kernels, upper half-space, potentials, homogeneous groups, trace inequality, boundedness, compactness, weights
First Page
119
Last Page
135
Recommended Citation
ASHRAF, USMAN; ASIF, MUHAMMAD; and MESKHI, ALEXANDER
(2014)
"Kernel operators on the upper half-space: boundedness and compactness criteria,"
Turkish Journal of Mathematics: Vol. 38:
No.
1, Article 11.
https://doi.org/10.3906/mat-1209-21
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss1/11
